Background

This analysis document compliments FIA NLS Models: Biomass Growth vs. Biomass. All of the background information from that document applies to these analyses, which are extensions to them. The difference between that document and this analysis is the use of different data subsets.

Here, we fit the models using: 1) a temporally-balanced dataset, where we take the first and most-recent plot record for all plots in the dataset, 2) a temporally-balanced dataset (same as #1), but which excludes plot locations which have experienced harvest (at any point over the study interval 2000-2022)

Below the model fitting procedure is implemented by ecoprovince:

Temporally-balancing the biomass growth data set

Lets look at some quick attributes of the dataset

  • The data set has 115221 observations, comprised of 58079 plots.
  • The frequency of growth measurements among plots is as follows (n=1 through 5): 25558, 13784, 12967, 5656, 114.
  • Thus 55.99% of plots have at least two growth measurements.

Analysis 1: Temporally-balanced analysis

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   4795     4394.3                                
## 2   4794     4389.9  1   4.362   4.7636 0.02912 *  
## 3   4793     4205.8  1 184.087 209.7877 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18612.85
## 2     2 18610.08
## 3     3 18406.54
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.017420   0.175129   0.099   0.9208    
## phi   0.009372   0.005673   1.652   0.0986 .  
## alpha 0.630415   0.040841  15.436   <2e-16 ***
## A     3.616767   0.127197  28.434   <2e-16 ***
## k     7.358455   0.782101   9.409   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9367 on 4793 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 2.987e-06
##   (36 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1   4793     4205.8                              
## 2   4792     4197.9  1 7.8859  9.0019 0.002711 **
## 3   4792     4196.7  0 0.0000                    
## 4   4791     4196.7  1 0.0049  0.0056 0.940386   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 18406.54
## 2    3a 18399.54
## 3    3b 18398.14
## 4    3c 18400.13
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.021936   0.175098   0.125     0.90    
## phi   0.008568   0.005660   1.514     0.13    
## alpha 0.626665   0.040848  15.341  < 2e-16 ***
## A     4.060029   0.280764  14.461  < 2e-16 ***
## k     7.729586   1.548545   4.992 6.20e-07 ***
## s     0.604862   0.108904   5.554 2.94e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9358 on 4792 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 5.013e-06
##   (36 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92609, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -8.5575, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 21 rows containing missing values (geom_point).
## Warning: Removed 1050 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value    Pr(>F)    
## 1   9777     9697.8                                 
## 2   9775     9681.2  2  16.60   8.3794 0.0002312 ***
## 3   9774     9053.6  1 627.57 677.5012 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 35844.15
## 2     2 35826.64
## 3     3 35173.25
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.905672   0.202832   4.465 8.09e-06 ***
## phi    0.019056   0.004331   4.400 1.09e-05 ***
## alpha  0.811354   0.028498  28.471  < 2e-16 ***
## A      2.661009   0.095088  27.985  < 2e-16 ***
## k     10.143277   0.592955  17.106  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9624 on 9774 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.105e-06
##   (3197 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   9774     9053.6                                
## 2   9773     8973.6  1 80.041 87.1715 < 2.2e-16 ***
## 3   9773     8981.2  0  0.000                      
## 4   9772     8972.1  1  9.060  9.8678  0.001687 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 35173.25
## 2    3a 35088.42
## 3    3b 35096.66
## 4    3c 35088.79
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.904464   0.201785   4.482 7.47e-06 ***
## phi    0.019060   0.004299   4.434 9.35e-06 ***
## alpha  0.804226   0.028323  28.395  < 2e-16 ***
## A      2.842362   0.106915  26.585  < 2e-16 ***
## k     21.910164   2.331017   9.399  < 2e-16 ***
## p      0.211069   0.018502  11.408  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9582 on 9773 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 1.087e-06
##   (3197 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1578 rows containing missing values (geom_point).
## Warning: Removed 1031 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5424     7458.3                                 
## 2   5423     7443.2  1  15.115  11.013 0.0009108 ***
## 3   5422     7169.6  1 273.579 206.893 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 24022.47
## 2     2 24013.46
## 3     3 23812.23
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.858152   0.137341  -6.248 4.46e-10 ***
## phi    0.018698   0.006456   2.896  0.00379 ** 
## alpha  0.711059   0.046491  15.295  < 2e-16 ***
## A      5.179889   0.188163  27.529  < 2e-16 ***
## k     15.877043   1.973121   8.047 1.04e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 5422 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 6.631e-06
##   (35 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   5422     7169.6                                
## 2   5421     7110.0  1  59.66  45.488 1.696e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 23812.23
## 2    3a 23768.88
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.922607   0.133022  -6.936 4.51e-12 ***
## phi     0.019262   0.006429   2.996  0.00275 ** 
## alpha   0.710211   0.045749  15.524  < 2e-16 ***
## A       7.872409   1.080917   7.283 3.73e-13 ***
## k     245.381353 102.237357   2.400  0.01642 *  
## p       0.362923   0.036056  10.066  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.145 on 5421 degrees of freedom
## 
## Number of iterations to convergence: 19 
## Achieved convergence tolerance: 9.037e-06
##   (35 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 16 rows containing missing values (geom_point).
## Warning: Removed 1036 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   2742     3071.9                                
## 2   2741     3066.0  1   5.924   5.2961 0.02145 *  
## 3   2740     2856.2  1 209.815 201.2809 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 11096.73
## 2     2 11093.43
## 3     3 10900.85
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.20088    0.27196  -0.739   0.4602    
## phi    0.02711    0.01188   2.282   0.0226 *  
## alpha  0.84796    0.05418  15.650   <2e-16 ***
## A      4.35985    0.24407  17.863   <2e-16 ***
## k     19.77609    2.04423   9.674   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.021 on 2740 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 8.797e-06
##   (809 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2740     2856.2                                
## 2   2739     2784.3  1 71.864  70.695 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 10900.85
## 2    3a 10832.89
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.17281    0.27101  -0.638 0.523747    
## phi     0.02009    0.01146   1.753 0.079635 .  
## alpha   0.83616    0.05343  15.649  < 2e-16 ***
## A       6.76142    0.75296   8.980  < 2e-16 ***
## k     163.39875   43.41256   3.764 0.000171 ***
## p       0.23907    0.01971  12.127  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.008 on 2739 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 3.685e-06
##   (809 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89438, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.4786, p-value = 4.287e-08
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 422 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value  Pr(>F)    
## 1   5267     6923.8                               
## 2   5266     6915.7  1   8.11   6.1755 0.01298 *  
## 3   5265     6729.8  1 185.93 145.4637 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 22279.18
## 2     2 22275.00
## 3     3 22133.38
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.90464    0.13883  -6.516 7.88e-11 ***
## phi   -0.02165    0.00849  -2.550   0.0108 *  
## alpha  0.65824    0.05115  12.870  < 2e-16 ***
## A      5.65960    0.23285  24.305  < 2e-16 ***
## k     34.88900    3.58050   9.744  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.131 on 5265 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.169e-06
##   (1120 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   singular gradient
##   model      AIC
## 1     3 22133.38
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.90464    0.13883  -6.516 7.88e-11 ***
## phi   -0.02165    0.00849  -2.550   0.0108 *  
## alpha  0.65824    0.05115  12.870  < 2e-16 ***
## A      5.65960    0.23285  24.305  < 2e-16 ***
## k     34.88900    3.58050   9.744  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.131 on 5265 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 9.169e-06
##   (1120 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 558 rows containing missing values (geom_point).
## Warning: Removed 1002 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value  Pr(>F)    
## 1   8057      19562                                
## 2   8056      19555  1    6.95   2.8618 0.09074 .  
## 3   8055      17895  1 1659.77 747.0906 < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 42193.22
## 2     2 42192.36
## 3     3 41479.47
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.814066   0.185610   4.386 1.17e-05 ***
## phi   0.003486   0.005940   0.587    0.557    
## alpha 0.871461   0.028993  30.058  < 2e-16 ***
## A     4.558598   0.149590  30.474  < 2e-16 ***
## k     1.767603   0.277782   6.363 2.08e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.491 on 8055 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 8.509e-06
##   (140 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   8055      17895                                
## 2   8054      17815  1 80.521  36.403 1.675e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 41479.47
## 2    3a 41445.12
## 3    3b 41438.25
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.712715   0.179272   3.976 7.08e-05 ***
## phi    0.003346   0.005912   0.566   0.5714    
## alpha  0.870534   0.028740  30.290  < 2e-16 ***
## A      7.785773   3.245462   2.399   0.0165 *  
## k     19.088949  77.814643   0.245   0.8062    
## s      0.206994   0.097156   2.131   0.0332 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.487 on 8054 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 4.67e-06
##   (140 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 72 rows containing missing values (geom_point).
## Warning: Removed 1017 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq  F value Pr(>F)    
## 1   8011      21190                              
## 2   8010      21183  1    6.7   2.5316 0.1116    
## 3   8009      19444  1 1738.8 716.1909 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 41553.79
## 2     2 41553.26
## 3     3 40868.87
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.680994   0.201717   3.376 0.000739 ***
## phi   0.001027   0.006109   0.168 0.866521    
## alpha 0.871185   0.029193  29.842  < 2e-16 ***
## A     4.601909   0.173334  26.549  < 2e-16 ***
## k     7.180785   0.651847  11.016  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.558 on 8009 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 5.547e-06
##   (180 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)    
## 1   8009      19444                               
## 2   8008      19235  1 209.897 87.3873 < 2e-16 ***
## 3   8008      19239  0   0.000                    
## 4   8007      19231  1   8.249  3.4346 0.06388 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 40868.87
## 2    3a 40783.89
## 3    3b 40785.71
## 4    3c 40784.27
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     0.6269578  0.1962586   3.195  0.00141 ** 
## phi   -0.0004434  0.0060463  -0.073  0.94154    
## alpha  0.8634163  0.0287793  30.001  < 2e-16 ***
## A      5.1542031  0.2207891  23.344  < 2e-16 ***
## k     32.7456324  6.0571195   5.406 6.63e-08 ***
## p      0.3644776  0.0261755  13.924  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.55 on 8008 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 4.497e-06
##   (180 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 87 rows containing missing values (geom_point).
## Warning: Removed 931 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Error in nls(fg_2, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model      AIC
## 1     1 4393.881
## 2     2       NA
## 3     3 4348.439
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.30681    1.22127   1.070    0.285    
## phi   -0.01652    0.02677  -0.617    0.537    
## alpha  0.83358    0.10515   7.928 7.21e-15 ***
## A      3.81431    0.76070   5.014 6.52e-07 ***
## k      1.86697    1.30984   1.425    0.154    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.604 on 828 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 9.459e-06
##   (29 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: does not fit
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 4348.439
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.30681    1.22127   1.070    0.285    
## phi   -0.01652    0.02677  -0.617    0.537    
## alpha  0.83358    0.10515   7.928 7.21e-15 ***
## A      3.81431    0.76070   5.014 6.52e-07 ***
## k      1.86697    1.30984   1.425    0.154    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.604 on 828 degrees of freedom
## 
## Number of iterations to convergence: 18 
## Achieved convergence tolerance: 9.459e-06
##   (29 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90981, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.7773, p-value = 0.005481
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 15 rows containing missing values (geom_point).
## Warning: Removed 645 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1    979     1429.8                               
## 2    978     1429.8  1  0.0483  0.0330 0.855861   
## 3    977     1418.2  1 11.5087  7.9281 0.004965 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 4162.017
## 2     2 4163.983
## 3     3 4158.047
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.070204   0.602700   0.116  0.90729    
## phi   -0.007581   0.017898  -0.424  0.67199    
## alpha  0.459818   0.155166   2.963  0.00312 ** 
## A      3.386890   0.428713   7.900 7.47e-15 ***
## k     12.024248   3.777479   3.183  0.00150 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.205 on 977 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 6.046e-06
##   (412 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     3 4158.047
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.070204   0.602700   0.116  0.90729    
## phi   -0.007581   0.017898  -0.424  0.67199    
## alpha  0.459818   0.155166   2.963  0.00312 ** 
## A      3.386890   0.428713   7.900 7.47e-15 ***
## k     12.024248   3.777479   3.183  0.00150 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.205 on 977 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 6.046e-06
##   (412 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.71976, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.0823, p-value = 0.03732
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 220 rows containing missing values (geom_point).
## Warning: Removed 1176 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    107     383.70                            
## 2    106     371.31  1 12.387  3.5362 0.06279 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1       NA
## 2     2 449.6049
## 3     3 447.9623
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge    -0.003205   7.346050   0.000   0.9997  
## phi    0.360038   0.192061   1.875   0.0636 .
## alpha  0.995614   0.450664   2.209   0.0293 *
## A      0.714946   1.067535   0.670   0.5045  
## k      6.442888  12.204161   0.528   0.5987  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.872 on 106 degrees of freedom
## 
## Number of iterations to convergence: 21 
## Achieved convergence tolerance: 9.792e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': s
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': s
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    106     371.31                         
## 2    105     371.17  1 0.1343   0.038 0.8458
##   model      AIC
## 1     3 447.9623
## 2    3a 449.9222
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)  
## ge    -0.003205   7.346050   0.000   0.9997  
## phi    0.360038   0.192061   1.875   0.0636 .
## alpha  0.995614   0.450664   2.209   0.0293 *
## A      0.714946   1.067535   0.670   0.5045  
## k      6.442888  12.204161   0.528   0.5987  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.872 on 106 degrees of freedom
## 
## Number of iterations to convergence: 21 
## Achieved convergence tolerance: 9.792e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.70407, p-value = 1.192e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.56475, p-value = 0.5722
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1282 row(s) containing missing values (geom_path).

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    136     120.26                          
## 2    135     119.67  1 0.58613  0.6612 0.4176
## 3    134     117.29  1 2.38196  2.7213 0.1014
##   model      AIC
## 1     1 459.1608
## 2     2 460.4817
## 3     3 459.6871
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)  
## ge   0.4799     1.7461   0.275   0.7839  
## A    3.4663     1.3351   2.596   0.0105 *
## k   62.4630    26.3410   2.371   0.0191 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9403 on 136 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 8.801e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    136     120.26                            
## 2    135     117.70  1 2.5603  2.9366 0.08889 .
## 3    135     118.66  0 0.0000                  
## 4    134     117.39  1 1.2740  1.4542 0.22997  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 459.1608
## 2    1a 458.1696
## 3    1b 459.3057
## 4    1c 459.8054
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * 
##     A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## ge   0.33561    1.63267   0.206   0.8374  
## A    4.90376    2.82747   1.734   0.0851 .
## k  166.96848  159.88931   1.044   0.2982  
## p    0.10369    0.04841   2.142   0.0340 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9337 on 135 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.644e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90099, p-value = 3.898e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.0874, p-value = 0.03685
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 9 rows containing missing values (geom_point).
## Warning: Removed 1140 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(fg_1, data = G_342, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   5087     4233.1                                 
## 2   5086     4213.2  1  19.876  23.993 9.968e-07 ***
## 3   5085     3988.2  1 225.054 286.949 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19222.23
## 2     2 19200.27
## 3     3 18922.85
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     0.80095    0.22370   3.580 0.000346 ***
## phi    0.01711    0.00514   3.329 0.000879 ***
## alpha  0.63264    0.03477  18.195  < 2e-16 ***
## A      2.89265    0.11960  24.186  < 2e-16 ***
## k      2.67623    0.46800   5.718 1.14e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8856 on 5085 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.751e-06
##   (14 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1   5085     3988.2                           
## 2   5084     3985.4  1 2.7938  3.5640 0.0591 .
## 3   5084     3986.8  0 0.0000                 
## 4   5083     3985.1  1 1.6672  2.1265 0.1448  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 18922.85
## 2    3a 18921.29
## 3    3b 18923.11
## 4    3c 18922.98
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.794538   0.223161   3.560 0.000374 ***
## phi   0.016671   0.005141   3.243 0.001192 ** 
## alpha 0.633054   0.034748  18.218  < 2e-16 ***
## A     2.920326   0.122450  23.849  < 2e-16 ***
## k     4.756600   1.701132   2.796 0.005191 ** 
## p     0.271191   0.124863   2.172 0.029909 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8854 on 5084 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 9.458e-07
##   (14 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 5 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq  F value Pr(>F)    
## 1   5232      11548                               
## 2   5231      11544  1   3.721   1.6861 0.1942    
## 3   5230      11293  1 251.048 116.2620 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 25880.58
## 2     2 25880.89
## 3     3 25767.79
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.021668   0.212436  -0.102    0.919    
## phi   -0.008750   0.008883  -0.985    0.325    
## alpha  0.825669   0.072299  11.420   <2e-16 ***
## A      4.326398   0.198641  21.780   <2e-16 ***
## k      9.233071   2.088528   4.421    1e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.469 on 5230 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.067e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 25767.79
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.021668   0.212436  -0.102    0.919    
## phi   -0.008750   0.008883  -0.985    0.325    
## alpha  0.825669   0.072299  11.420   <2e-16 ***
## A      4.326398   0.198641  21.780   <2e-16 ***
## k      9.233071   2.088528   4.421    1e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.469 on 5230 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 7.067e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 13 rows containing missing values (geom_point).
## Warning: Removed 982 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    598     960.81                                 
## 2    597     960.07  1  0.7388  0.4594    0.4982    
## 3    596     931.53  1 28.5416 18.2611 2.242e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2572.128
## 2     2 2573.666
## 3     3 2557.528
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    2.907462   1.857044   1.566    0.118    
## phi   0.006323   0.033208   0.190    0.849    
## alpha 0.960964   0.207502   4.631 4.47e-06 ***
## A     1.927068   0.465506   4.140 3.98e-05 ***
## k     9.122929   6.170366   1.479    0.140    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.25 on 596 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 6.326e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    596     931.53                            
## 2    595     926.65  1 4.8783  3.1324 0.07726 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 2557.528
## 2    3a 2556.372
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    3.087e+00  1.931e+00   1.599    0.110    
## phi   3.113e-03  3.267e-02   0.095    0.924    
## alpha 9.711e-01  2.038e-01   4.766 2.36e-06 ***
## A     4.942e+00  1.758e+01   0.281    0.779    
## k     8.449e+02  5.159e+03   0.164    0.870    
## p     2.656e-01  8.955e-01   0.297    0.767    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.248 on 595 degrees of freedom
## 
## Number of iterations to convergence: 14 
## Achieved convergence tolerance: 6.996e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92974, p-value = 3.585e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.9579, p-value = 0.3381
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 3 rows containing missing values (geom_point).
## Warning: Removed 1175 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1    668     936.72                                
## 2    667     920.45  1 16.274  11.793 0.0006314 ***
## 3    666     885.05  1 35.402  26.640  3.24e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2792.478
## 2     2 2782.718
## 3     3 2758.401
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.44313    2.33472   1.475 0.140753    
## phi    0.07010    0.03005   2.333 0.019970 *  
## alpha  0.88785    0.15922   5.576 3.58e-08 ***
## A      1.64621    0.47232   3.485 0.000524 ***
## k      3.70623    2.06642   1.794 0.073339 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.153 on 666 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 5.306e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 2758.401
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     3.44313    2.33472   1.475 0.140753    
## phi    0.07010    0.03005   2.333 0.019970 *  
## alpha  0.88785    0.15922   5.576 3.58e-08 ***
## A      1.64621    0.47232   3.485 0.000524 ***
## k      3.70623    2.06642   1.794 0.073339 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.153 on 666 degrees of freedom
## 
## Number of iterations to convergence: 15 
## Achieved convergence tolerance: 5.306e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.95762, p-value = 5.457e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.9997, p-value = 6.343e-05
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1218 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)   
## 1    165     194.45                             
## 2    164     185.13  1 9.3239  8.2598 0.00459 **
## 3    163     181.44  1 3.6902  3.3152 0.07047 . 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 584.8960
## 2     2 578.6409
## 3     3 577.2582
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.53555    4.43455  -0.121 0.904025    
## phi     0.16308    0.04179   3.902 0.000139 ***
## alpha   0.71187    0.36243   1.964 0.051211 .  
## A      16.71690   21.70358   0.770 0.442274    
## k     413.64399  385.93166   1.072 0.285391    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.055 on 163 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.708e-06
##   (172 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M261,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    163     181.44                          
## 2    162     180.72  1 0.71284   0.639 0.4252
##   model      AIC
## 1     3 577.2582
## 2    3a 578.5969
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.53555    4.43455  -0.121 0.904025    
## phi     0.16308    0.04179   3.902 0.000139 ***
## alpha   0.71187    0.36243   1.964 0.051211 .  
## A      16.71690   21.70358   0.770 0.442274    
## k     413.64399  385.93166   1.072 0.285391    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.055 on 163 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 1.708e-06
##   (172 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96414, p-value = 0.0002509
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.5878, p-value = 0.1123
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 81 rows containing missing values (geom_point).
## Warning: Removed 1274 row(s) containing missing values (geom_path).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1    217     220.35                                 
## 2    216     220.32  1  0.0274  0.0269      0.87    
## 3    215     199.25  1 21.0776 22.7442 3.411e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 664.8357
## 2     2 666.8083
## 3     3 646.6857
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.86821    5.35113   0.536  0.59251    
## phi   -0.04321    0.04806  -0.899  0.36953    
## alpha  0.90060    0.15821   5.693 4.07e-08 ***
## A      1.70528    1.17880   1.447  0.14946    
## k     39.64935   14.75062   2.688  0.00775 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9627 on 215 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 9.633e-06
##   (90 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    215     199.25                             
## 2    214     199.16  1 0.09064  0.0974 0.75528  
## 3    214     197.84  0 0.00000                  
## 4    213     194.91  1 2.93804  3.2108 0.07457 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 646.6857
## 2    3a 648.5856
## 3    3b 647.1336
## 4    3c 645.8421
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     1.95469    4.16003   0.470   0.6389    
## phi   -0.03914    0.04751  -0.824   0.4110    
## alpha  0.91363    0.15593   5.859 1.75e-08 ***
## A      1.45952    0.86394   1.689   0.0926 .  
## k     35.13504    6.47183   5.429 1.54e-07 ***
## p      0.22941    0.10064   2.279   0.0236 *  
## s      3.02467    1.67678   1.804   0.0727 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9566 on 213 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 3.834e-06
##   (90 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.7338, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 0.0049161, p-value = 0.9961
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 41 rows containing missing values (geom_point).
## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3b
212 Laurentian Mixed Forest 3a
221 Eastern Broadleaf Forest 3a
222 Midwest Broadleaf Forest 3a
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3b
232 Outer Coastal Plain Mixed Forest 3a
234 Lower Mississippi Riverine Forest 3
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 3
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 3
332 Great Plains Steppe 1a
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3a
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 3a
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 3c
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 4834 2417 0.0219361 0.0306593 -0.3213364 0.3652087 0.0085678 0.0000320 -0.0025282 0.0196638 0.6266651 0.0016686 0.5465834 0.7067468 4.0600295 3.5096040 4.610455 7.729586 4.6937264 10.765446
212 Laurentian Mixed Forest east 12976 6488 0.9044638 0.0407172 0.5089233 1.3000042 0.0190601 0.0000185 0.0106337 0.0274864 0.8042261 0.0008022 0.7487076 0.8597447 2.8423616 2.6327869 3.051936 21.910164 17.3408884 26.479440
221 Eastern Broadleaf Forest east 5462 2731 -0.9226068 0.0176949 -1.1833838 -0.6618298 0.0192624 0.0000413 0.0066591 0.0318656 0.7102109 0.0020930 0.6205242 0.7998976 7.8724086 5.7533770 9.991440 245.381353 44.9550652 445.807640
222 Midwest Broadleaf Forest east 3554 1777 -0.1728129 0.0734466 -0.7042182 0.3585924 0.0200879 0.0001312 -0.0023757 0.0425515 0.8361600 0.0028550 0.7313887 0.9409313 6.7614239 5.2849897 8.237858 163.398751 78.2740742 248.523429
223 Central Interior Broadleaf Forest east 6390 3195 -0.9046411 0.0192728 -1.1767988 -0.6324833 -0.0216540 0.0000721 -0.0382987 -0.0050092 0.6582379 0.0026159 0.5579699 0.7585059 5.6595971 5.2031064 6.116088 34.888998 27.8697324 41.908263
231 Southeastern Mixed Forest east 8200 4100 0.7127154 0.0321384 0.3612961 1.0641348 0.0033457 0.0000349 -0.0082427 0.0149341 0.8705342 0.0008260 0.8141957 0.9268727 7.7857734 1.4238278 14.147719 19.088949 -133.4478718 171.625770
232 Outer Coastal Plain Mixed Forest east 8194 4097 0.6269578 0.0385174 0.2422398 1.0116757 -0.0004434 0.0000366 -0.0122957 0.0114089 0.8634163 0.0008283 0.8070013 0.9198313 5.1542031 4.7213990 5.587007 32.745632 20.8721017 44.619163
234 Lower Mississippi Riverine Forest east 862 431 1.3068089 1.4915046 -1.0903437 3.7039615 -0.0165220 0.0007167 -0.0690687 0.0360248 0.8335760 0.0110563 0.6271865 1.0399655 3.8143143 2.3211796 5.307449 1.866965 -0.7040329 4.437963
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1394 697 0.0702036 0.3632469 -1.1125312 1.2529385 -0.0075807 0.0003203 -0.0427043 0.0275428 0.4598175 0.0240765 0.1553206 0.7643145 3.3868899 2.5455865 4.228193 12.024248 4.6113426 19.437154
255 Prairie Parkland (Subtropical) east 446 223 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 -0.0032054 53.9644522 -14.5674642 14.5610534 0.3600378 0.0368875 -0.0207424 0.7408180 0.9956138 0.2030977 0.1021294 1.8890982 0.7149459 -1.4015470 2.831439 6.442888 -17.7530487 30.638824
332 Great Plains Steppe interior west 154 77 0.3356066 2.6656092 -2.8933109 3.5645242 NA NA NA NA NA NA NA NA 4.9037624 -0.6881114 10.495636 166.968483 -149.2433635 483.180329
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5104 2552 0.7945375 0.0498009 0.3570456 1.2320294 0.0166711 0.0000264 0.0065922 0.0267501 0.6330542 0.0012074 0.5649327 0.7011756 2.9203257 2.6802712 3.160380 4.756600 1.4216476 8.091552
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5262 2631 -0.0216677 0.0451289 -0.4381302 0.3947949 -0.0087496 0.0000789 -0.0261642 0.0086650 0.8256690 0.0052271 0.6839333 0.9674046 4.3263978 3.9369778 4.715818 9.233071 5.1386843 13.327457
M223 Ozark Broadleaf Forest Meadow east 604 302 3.0869142 3.7275330 -0.7048661 6.8786944 0.0031133 0.0010675 -0.0610551 0.0672817 0.9711097 0.0415158 0.5709447 1.3712748 4.9423202 -29.5874030 39.472043 844.913093 -9286.7227176 10976.548904
M231 Ouachita Mixed Forest east 678 339 3.4431258 5.4509268 -1.1411763 8.0274279 0.0700954 0.0009031 0.0110886 0.1291022 0.8878522 0.0253518 0.5752136 1.2004909 1.6462128 0.7187955 2.573630 3.706232 -0.3512556 7.763719
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 340 170 -0.5355458 19.6652227 -9.2921150 8.2210234 0.1630850 0.0017465 0.0805634 0.2456065 0.7118723 0.1313551 -0.0037899 1.4275345 16.7169000 -26.1395256 59.573326 413.643995 -348.4261661 1175.714155
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 310 155 1.9546861 17.3058093 -6.2454053 10.1547774 -0.0391386 0.0022576 -0.1327974 0.0545202 0.9136298 0.0243144 0.6062644 1.2209951 1.4595174 -0.2434567 3.162492 35.135035 22.3779877 47.892083
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning: package 'ggnewscale' was built under R version 4.2.1
## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database

## Warning in grid.Call(C_stringMetric, as.graphicsAnnot(x$label)): font family not
## found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 19 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 19 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region  weighted.ge weighted.ge.std_Error 95 % CI, upper
## 1     entire US  0.326397599            0.08068344     0.48453714
## 2       pacific -0.002799508            0.02318112     0.04263549
## 3          east  0.319091977            0.07339462     0.46294543
## 4 interior west  0.010105130            0.02420088     0.05753885
##   95 % CI, lower
## 1     0.16825806
## 2    -0.04823451
## 3     0.17523852
## 4    -0.03732859

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US 0.0076907481           0.0021886250    0.011980453
## 2       pacific 0.0008525089           0.0002184578    0.001280686
## 3          east 0.0063715946           0.0021376764    0.010561440
## 4 interior west 0.0004666446           0.0004155660    0.001281154
##   95 % CI, lower
## 1   0.0034010431
## 2   0.0004243315
## 3   0.0021817489
## 4  -0.0003478647

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.761073471              0.013481268    0.787496757
## 2       pacific    0.003721235              0.001894561    0.007434575
## 3          east    0.751191484              0.013301670    0.777262757
## 4 interior west    0.006160752              0.001104898    0.008326353
##   95 % CI, lower
## 1   7.346502e-01
## 2   7.895873e-06
## 3   7.251202e-01
## 4   3.995151e-03

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   4.958899
## 2       pacific  15.036365
## 3          east   4.928638
## 4 interior west   2.025068

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US   56.46396
## 2       pacific  372.06074
## 3          east   54.57977
## 4 interior west   58.56625

Analysis 2: Temporally-balanced, No-harvest

211 - Northeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   3724     3417.2                                 
## 2   3723     3415.4  1  1.7416  1.8984    0.1683    
## 3   3722     3389.8  1 25.6472 28.1609 1.182e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 14508.81
## 2     2 14508.91
## 3     3 14482.82
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.061176   0.195351  -0.313    0.754    
## phi    0.008549   0.006482   1.319    0.187    
## alpha  0.535540   0.096853   5.529 3.43e-08 ***
## A      3.611084   0.145354  24.843  < 2e-16 ***
## k      7.244637   0.861095   8.413  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9543 on 3722 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 1.2e-06
##   (33 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   3722     3389.8                             
## 2   3721     3386.8  1 2.96148  3.2537 0.07134 .
## 3   3721     3386.4  0 0.00000                  
## 4   3720     3386.3  1 0.02915  0.0320 0.85799  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 14482.82
## 2    3a 14481.56
## 3    3b 14481.06
## 4    3c 14483.03
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.070178   0.194544  -0.361    0.718    
## phi    0.008132   0.006476   1.256    0.209    
## alpha  0.523308   0.097010   5.394 7.31e-08 ***
## A      3.856032   0.234882  16.417  < 2e-16 ***
## k      7.213084   1.172636   6.151 8.50e-10 ***
## s      0.728282   0.126280   5.767 8.72e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.954 on 3721 degrees of freedom
## 
## Number of iterations to convergence: 5 
## Achieved convergence tolerance: 3.466e-06
##   (33 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.91809, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.9894, p-value = 1.356e-15
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 17 rows containing missing values (geom_point).
## Warning: Removed 1050 row(s) containing missing values (geom_path).

plotting 2

212 - Laurentian Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7890     7621.3                                
## 2   7888     7609.9  2 11.427  5.9224  0.002691 ** 
## 3   7887     7515.5  1 94.440 99.1083 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 28703.69
## 2     2 28691.08
## 3     3 28594.53
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.661266   0.210736   3.138 0.001708 ** 
## phi    0.017165   0.004916   3.492 0.000483 ***
## alpha  0.604017   0.057787  10.452  < 2e-16 ***
## A      2.776878   0.109209  25.427  < 2e-16 ***
## k     12.517190   0.773306  16.187  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9762 on 7887 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 3.292e-06
##   (2590 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   7887     7515.5                                
## 2   7886     7446.3  1 69.176  73.261 < 2.2e-16 ***
## 3   7886     7458.6  0  0.000                      
## 4   7885     7446.2  1 12.393  13.123 0.0002935 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 28594.53
## 2    3a 28523.55
## 3    3b 28536.56
## 4    3c 28525.43
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.646031   0.208501   3.098 0.001952 ** 
## phi    0.017151   0.004879   3.516 0.000441 ***
## alpha  0.574743   0.057239  10.041  < 2e-16 ***
## A      2.983290   0.124616  23.940  < 2e-16 ***
## k     25.199015   2.781625   9.059  < 2e-16 ***
## p      0.184660   0.018056  10.227  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9717 on 7886 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 5.487e-06
##   (2590 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 1290 rows containing missing values (geom_point).
## Warning: Removed 1031 row(s) containing missing values (geom_path).

plotting 2

221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4441     6146.1                                
## 2   4440     6136.9  1  9.215  6.6671  0.009853 ** 
## 3   4439     6077.3  1 59.583 43.5207 4.687e-11 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 19769.06
## 2     2 19764.39
## 3     3 19723.04
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.932344   0.148924  -6.261 4.20e-10 ***
## phi    0.017404   0.007245   2.402   0.0163 *  
## alpha  0.597913   0.087478   6.835 9.31e-12 ***
## A      5.282777   0.215420  24.523  < 2e-16 ***
## k     17.411747   2.294852   7.587 3.96e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.17 on 4439 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 3.699e-06
##   (32 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4439     6077.3                                
## 2   4438     6034.4  1 42.924  31.568 2.043e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 19723.04
## 2    3a 19693.54
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##         Estimate Std. Error t value Pr(>|t|)    
## ge     -0.999615   0.144158  -6.934 4.68e-12 ***
## phi     0.018283   0.007219   2.533   0.0114 *  
## alpha   0.586230   0.086062   6.812 1.09e-11 ***
## A       7.616262   0.951330   8.006 1.50e-15 ***
## k     199.643588  80.493759   2.480   0.0132 *  
## p       0.355542   0.031621  11.244  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.166 on 4438 degrees of freedom
## 
## Number of iterations to convergence: 21 
## Achieved convergence tolerance: 6.352e-06
##   (32 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87687, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -11.809, p-value < 2.2e-16
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 16 rows containing missing values (geom_point).
## Warning: Removed 1036 row(s) containing missing values (geom_path).

plotting 2

222 - Midwest Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2144     2308.5                                
## 2   2143     2307.0  1  1.544  1.4338    0.2313    
## 3   2142     2242.6  1 64.325 61.4388 7.137e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 8572.838
## 2     2 8573.402
## 3     3 8514.686
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    -0.32181    0.29422  -1.094    0.274    
## phi    0.02115    0.01326   1.595    0.111    
## alpha  0.77021    0.09118   8.447   <2e-16 ***
## A      4.43549    0.27650  16.042   <2e-16 ***
## k     20.77089    2.32347   8.940   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.023 on 2142 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.419e-06
##   (651 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   2142     2242.6                                
## 2   2141     2193.0  1 49.663  48.486 4.407e-12 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 8514.686
## 2    3a 8468.606
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.33719    0.28878  -1.168 0.243088    
## phi     0.01668    0.01292   1.291 0.196742    
## alpha   0.73132    0.08996   8.129 7.22e-16 ***
## A       6.15292    0.62215   9.890  < 2e-16 ***
## k     112.11832   28.80770   3.892 0.000102 ***
## p       0.22900    0.01975  11.592  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.012 on 2141 degrees of freedom
## 
## Number of iterations to convergence: 11 
## Achieved convergence tolerance: 4.252e-06
##   (651 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.90538, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -5.8645, p-value = 4.505e-09
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 337 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

223 - Central Interior Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4276     5695.6                                
## 2   4275     5689.5  1  6.016  4.5199   0.03356 *  
## 3   4274     5652.3  1 37.236 28.1558 1.176e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 18182.73
## 2     2 18180.21
## 3     3 18154.12
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.027146   0.148119  -6.935 4.69e-12 ***
## phi   -0.018540   0.009594  -1.932   0.0534 .  
## alpha  0.534425   0.097121   5.503 3.96e-08 ***
## A      5.643824   0.256697  21.986  < 2e-16 ***
## k     33.306989   3.856155   8.637  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 4274 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 7.797e-06
##   (843 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223,  : 
##   singular gradient
##   model      AIC
## 1     3 18154.12
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -1.027146   0.148119  -6.935 4.69e-12 ***
## phi   -0.018540   0.009594  -1.932   0.0534 .  
## alpha  0.534425   0.097121   5.503 3.96e-08 ***
## A      5.643824   0.256697  21.986  < 2e-16 ***
## k     33.306989   3.856155   8.637  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.15 on 4274 degrees of freedom
## 
## Number of iterations to convergence: 13 
## Achieved convergence tolerance: 7.797e-06
##   (843 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 425 rows containing missing values (geom_point).
## Warning: Removed 1002 row(s) containing missing values (geom_path).

plotting 2

231 - Southeastern Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   6314      14258                              
## 2   6313      14257  1   1.161  0.5141 0.4734    
## 3   6312      14074  1 182.371 81.7891 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 32889.13
## 2     2 32890.61
## 3     3 32811.28
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.710232   0.203322   3.493 0.000481 ***
## phi   0.004263   0.006685   0.638 0.523684    
## alpha 0.729345   0.076921   9.482  < 2e-16 ***
## A     4.570140   0.167694  27.253  < 2e-16 ***
## k     2.163263   0.355943   6.078 1.29e-09 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.493 on 6312 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 9.932e-06
##   (127 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   6312      14074                                
## 2   6311      14015  1 59.663  26.867 2.247e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 32811.28
## 2    3a 32786.45
## 3    3b 32778.17
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + 
##     B_plt_t1_MgHa^s))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    5.717e-01  1.940e-01   2.947  0.00322 ** 
## phi   4.120e-03  6.652e-03   0.619  0.53574    
## alpha 7.208e-01  7.617e-02   9.463  < 2e-16 ***
## A     8.132e+00  3.692e+00   2.203  0.02766 *  
## k     3.225e+01  1.361e+02   0.237  0.81269    
## s     2.182e-01  1.010e-01   2.160  0.03082 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.489 on 6311 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.27e-06
##   (127 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

predict and plot

## Warning: Removed 56 rows containing missing values (geom_point).
## Warning: Removed 1017 row(s) containing missing values (geom_path).

plotting 2

232 - Outer Coastal Plain Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   6387      15897                              
## 2   6386      15897  1   0.114  0.0458 0.8306    
## 3   6385      15679  1 217.981 88.7711 <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 33025.57
## 2     2 33027.52
## 3     3 32941.30
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.567799   0.222585   2.551   0.0108 *  
## phi   -0.001798   0.006881  -0.261   0.7938    
## alpha  0.671218   0.067521   9.941   <2e-16 ***
## A      4.670149   0.200119  23.337   <2e-16 ***
## k      8.928238   0.844911  10.567   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.567 on 6385 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 3.625e-06
##   (150 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)    
## 1   6385      15679                              
## 2   6384      15485  1 193.852 79.9204 <2e-16 ***
## 3   6384      15487  0   0.000                   
## 4   6383      15482  1   5.653  2.3307 0.1269    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 32941.30
## 2    3a 32863.80
## 3    3b 32864.87
## 4    3c 32864.54
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     0.499390   0.215028   2.322   0.0202 *  
## phi   -0.002996   0.006803  -0.440   0.6596    
## alpha  0.646923   0.065754   9.839  < 2e-16 ***
## A      5.337681   0.266692  20.014  < 2e-16 ***
## k     40.924127   8.094591   5.056 4.41e-07 ***
## p      0.346177   0.025730  13.454  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.557 on 6384 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 2.03e-06
##   (150 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

predict and plot

## Warning: Removed 85 rows containing missing values (geom_point).
## Warning: Removed 931 row(s) containing missing values (geom_path).

plotting 2

234 - Lower Mississippi Riverine Forest

model selection 1

## Error in nls(fg_3, data = G_234, start = c(ge = ge.start, phi = phi.start,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq   Df  Sum Sq F value Pr(>F)
## 1    684     1785.1                            
## 2    683     1785.0    1    0.09  0.0344 0.8529
## 3    828     2130.3 -145 -345.34  0.9113 0.7525
##   model      AIC
## 1     1 3613.269
## 2     2 3615.235
## 3     3 4348.439
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  0.30861    0.75079   0.411    0.681    
## A   3.98414    0.61078   6.523 1.34e-10 ***
## k   0.08395    0.22172   0.379    0.705    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.615 on 684 degrees of freedom
## 
## Number of iterations to convergence: 31 
## Achieved convergence tolerance: 6.138e-06
##   (27 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_234,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     1 3613.269
## 2    1a       NA
## 3    1b       NA
## 4    1c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  0.30861    0.75079   0.411    0.681    
## A   3.98414    0.61078   6.523 1.34e-10 ***
## k   0.08395    0.22172   0.379    0.705    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.615 on 684 degrees of freedom
## 
## Number of iterations to convergence: 31 
## Achieved convergence tolerance: 6.138e-06
##   (27 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.93351, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -2.4081, p-value = 0.01604
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 10 rows containing missing values (geom_point).
## Warning: Removed 645 row(s) containing missing values (geom_path).

plotting 2

242 - Pacific Lowland Mixed Forest

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_242$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_242.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

251 - Prairie Parkland (Temperate)

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)  
## 1    868     1343.8                           
## 2    867     1343.6  1 0.1880  0.1213 0.7277  
## 3    866     1338.4  1 5.2212  3.3783 0.0664 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 3738.098
## 2     2 3739.976
## 3     3 3738.585
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.2616     0.5324  -0.491  0.62333    
## A    3.4268     0.4412   7.767 2.27e-14 ***
## k   12.2112     4.1347   2.953  0.00323 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.244 on 868 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.062e-06
##   (349 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_251,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     1 3738.098
## 2    1a       NA
## 3    1b       NA
## 4    1c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge  -0.2616     0.5324  -0.491  0.62333    
## A    3.4268     0.4412   7.767 2.27e-14 ***
## k   12.2112     4.1347   2.953  0.00323 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.244 on 868 degrees of freedom
## 
## Number of iterations to convergence: 12 
## Achieved convergence tolerance: 7.062e-06
##   (349 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.70974, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.09, p-value = 0.002002
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 172 rows containing missing values (geom_point).
## Warning: Removed 1176 row(s) containing missing values (geom_path).

plotting 2

255 - Prairie Parkland (Subtropical)

model selection 1

## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

261 - California Coastal Chaparral Forest and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

262 - California Dry Steppe

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

263 - California Coastal Steppe - Mixed Forest and Redwood Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit

  • add s model: does not fit

  • add s+p model: does not fit

  • note: model fit, but fit was funky due to data being sparse

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

313 - Colorado Plateau Semi-Desert

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

315 - Southwest Plateau and Plains Dry Steppe and Shrub

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

321 - Chihuahuan Semi-Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

322 - American Semidesert and Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

331 - Great Plains/Palouse Dry Steppe

model selection 1

## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    103     336.76                         
## 2    102     329.06  1 7.6986  2.3864 0.1255
##   model      AIC
## 1     1       NA
## 2     2 428.6806
## 3     3 428.2061
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge      0.8754    10.2104   0.086   0.9318  
## phi     0.2478     0.1634   1.516   0.1325  
## alpha   1.0137     0.5820   1.742   0.0846 .
## A       0.7672     1.3237   0.580   0.5635  
## k       8.1068    12.9587   0.626   0.5330  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.796 on 102 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 5.172e-06
##   (7 observations deleted due to missingness)

summary

  • simple model: does not fit
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': s
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_331,  : 
##   parameters without starting value in 'data': s
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value Pr(>F)
## 1    102     329.06                           
## 2    101     328.98  1 0.086442  0.0265 0.8709
##   model      AIC
## 1     3 428.2061
## 2    3a 430.1780
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)  
## ge      0.8754    10.2104   0.086   0.9318  
## phi     0.2478     0.1634   1.516   0.1325  
## alpha   1.0137     0.5820   1.742   0.0846 .
## A       0.7672     1.3237   0.580   0.5635  
## k       8.1068    12.9587   0.626   0.5330  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.796 on 102 degrees of freedom
## 
## Number of iterations to convergence: 16 
## Achieved convergence tolerance: 5.172e-06
##   (7 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.71219, p-value = 3.482e-13
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.28711, p-value = 0.774
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 4 rows containing missing values (geom_point).
## Warning: Removed 1282 row(s) containing missing values (geom_path).

plotting 2

332 - Great Plains Steppe

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    128    101.432                          
## 2    127    100.933  1 0.49846  0.6272 0.4299
## 3    126     98.809  1 2.12414  2.7087 0.1023
##   model      AIC
## 1     1 420.8587
## 2     2 422.2134
## 3     3 421.4270
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)   
## ge  -0.0774     1.3362  -0.058  0.95390   
## A    4.0399     1.3733   2.942  0.00388 **
## k   62.1240    24.4299   2.543  0.01218 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8902 on 128 degrees of freedom
## 
## Number of iterations to convergence: 6 
## Achieved convergence tolerance: 1.433e-06
##   (15 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_332,  : 
##   number of iterations exceeded maximum of 50
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df   Sum Sq F value   Pr(>F)   
## 1    128    101.432                                
## 2    127     99.482  1   1.9499  2.4892 0.117115   
## 3    127    100.495  0   0.0000                    
## 4    134    117.390 -7 -16.8947  3.0501 0.005325 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 420.8587
## 2    1a 420.3159
## 3    1b 421.6435
## 4    1c 459.8054
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * 
##     A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##     Estimate Std. Error t value Pr(>|t|)  
## ge  -0.15678    1.28061  -0.122   0.9028  
## A    5.23502    2.51910   2.078   0.0397 *
## k  137.15133  114.31833   1.200   0.2325  
## p    0.09601    0.04778   2.010   0.0466 *
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8851 on 127 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 7.015e-06
##   (15 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.89534, p-value = 4.022e-08
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.8143, p-value = 0.06963
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 1140 row(s) containing missing values (geom_path).

plotting 2

341 - Intermountain Semi-desert & Desert

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

342 - Intermountain Semi-Desert

model selection 1

## Error in nls(fg_1, data = G_342, start = c(ge = ge.start, A = A.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_342, start = c(ge = ge.start, phi = phi.start,  : 
##   number of iterations exceeded maximum of 50
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_342$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_342.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

411 - Everglades

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value    Pr(>F)    
## 1   3950     3001.9                                 
## 2   3949     2994.8  1  7.1265  9.3972  0.002188 ** 
## 3   3948     2977.3  1 17.4463 23.1343 1.567e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model     AIC
## 1     1 14658.1
## 2     2 14650.7
## 3     3 14629.6
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.913698   0.261840   3.490 0.000489 ***
## phi   0.015744   0.005705   2.760 0.005810 ** 
## alpha 0.445253   0.089362   4.983 6.54e-07 ***
## A     2.761313   0.132765  20.799  < 2e-16 ***
## k     2.243935   0.460393   4.874 1.14e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8684 on 3948 degrees of freedom
## 
## Number of iterations to convergence: 8 
## Achieved convergence tolerance: 2.208e-06
##   (13 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1   3948     2977.3                             
## 2   3947     2974.4  1 2.88375  3.8267 0.05051 .
## 3   3947     2975.3  0 0.00000                  
## 4   3946     2974.4  1 0.87017  1.1544 0.28269  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 14629.60
## 2    3a 14627.77
## 3    3b 14628.90
## 4    3c 14629.75
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge    0.897226   0.260481   3.444 0.000578 ***
## phi   0.015087   0.005705   2.644 0.008217 ** 
## alpha 0.445392   0.089305   4.987 6.39e-07 ***
## A     2.798841   0.137033  20.425  < 2e-16 ***
## k     4.938187   2.215835   2.229 0.025897 *  
## p     0.346373   0.141286   2.452 0.014266 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8681 on 3947 degrees of freedom
## 
## Number of iterations to convergence: 4 
## Achieved convergence tolerance: 2.77e-06
##   (13 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.98118, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -7.4445, p-value = 9.73e-14
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 6 rows containing missing values (geom_point).
## Warning: Removed 1108 row(s) containing missing values (geom_path).

plotting 2

M221 - Eastern Broadleaf Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value    Pr(>F)    
## 1   4659      10327                                
## 2   4658      10325  1  2.481  1.1194    0.2901    
## 3   4657      10235  1 89.688 40.8084 1.843e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 23096.71
## 2     2 23097.59
## 3     3 23058.91
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.081319   0.221554  -0.367    0.714    
## phi   -0.009838   0.009441  -1.042    0.297    
## alpha  0.808623   0.121451   6.658 3.10e-11 ***
## A      4.344956   0.212225  20.473  < 2e-16 ***
## k      9.583534   2.270030   4.222 2.47e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.482 on 4657 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.044e-06
##   (26 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
##   model      AIC
## 1     3 23058.91
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge    -0.081319   0.221554  -0.367    0.714    
## phi   -0.009838   0.009441  -1.042    0.297    
## alpha  0.808623   0.121451   6.658 3.10e-11 ***
## A      4.344956   0.212225  20.473  < 2e-16 ***
## k      9.583534   2.270030   4.222 2.47e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.482 on 4657 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.044e-06
##   (26 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.87004, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -6.6975, p-value = 2.12e-11
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 18 rows containing missing values (geom_point).
## Warning: Removed 982 row(s) containing missing values (geom_path).

plotting 2

M223 - Ozark Broadleaf Forest Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value  Pr(>F)  
## 1    524     819.79                            
## 2    523     819.72  1 0.0704  0.0449 0.83225  
## 3    522     814.78  1 4.9447  3.1679 0.07568 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2249.276
## 2     2 2251.231
## 3     3 2250.042
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * 
##     B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)    
## ge   2.6216     1.6056   1.633   0.1031    
## A    2.0517     0.4973   4.126  4.3e-05 ***
## k   19.1597    10.5392   1.818   0.0696 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.251 on 524 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 6.363e-06
##   (3 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223,  : 
##   number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1    524     819.79                         
## 2    523     816.31  1 3.4847  2.2326 0.1357
##   model      AIC
## 1     1 2249.276
## 2    1a 2249.031
## 3    1b       NA
## 4    1c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (p * 
##     A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## 
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## ge   2.6617     1.6208   1.642    0.101
## A    3.6417     4.4794   0.813    0.417
## k  344.4875   976.8539   0.353    0.724
## p    0.3030     0.2936   1.032    0.303
## 
## Residual standard error: 1.249 on 523 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 5.736e-06
##   (3 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.92549, p-value = 1.685e-15
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -1.8578, p-value = 0.0632
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1175 row(s) containing missing values (geom_path).

plotting 2

M231 - Ouachita Mixed Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1    581     732.19                               
## 2    580     720.59  1 11.6017  9.3382 0.002347 **
## 3    579     714.19  1  6.3998  5.1884 0.023102 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 2364.027
## 2     2 2356.699
## 3     3 2353.489
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.72388    2.02426   1.346 0.178953    
## phi    0.07373    0.03230   2.283 0.022807 *  
## alpha  0.88790    0.36882   2.407 0.016379 *  
## A      2.11860    0.59337   3.570 0.000386 ***
## k     20.19953    6.69006   3.019 0.002645 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.111 on 579 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 8.836e-06
##   (4 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231,  : 
##   number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M231,  : 
##   step factor 0.000488281 reduced below 'minFactor' of 0.000976562
##   model      AIC
## 1     3 2353.489
## 2    3a       NA
## 3    3b       NA
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     2.72388    2.02426   1.346 0.178953    
## phi    0.07373    0.03230   2.283 0.022807 *  
## alpha  0.88790    0.36882   2.407 0.016379 *  
## A      2.11860    0.59337   3.570 0.000386 ***
## k     20.19953    6.69006   3.019 0.002645 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.111 on 579 degrees of freedom
## 
## Number of iterations to convergence: 22 
## Achieved convergence tolerance: 8.836e-06
##   (4 observations deleted due to missingness)

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.97154, p-value = 3.181e-09
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -3.6475, p-value = 0.0002648
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 2 rows containing missing values (geom_point).
## Warning: Removed 1218 row(s) containing missing values (geom_path).

plotting 2

M242 - Cascade Mixed Forest

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df Sum Sq F value   Pr(>F)   
## 1    156     186.49                              
## 2    155     176.83  1 9.6612  8.4687 0.004145 **
## 3    154     172.37  1 4.4610  3.9857 0.047651 * 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 555.0482
## 2     2 548.5899
## 3     3 546.5272
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.68834    4.20877  -0.164 0.870301    
## phi     0.16904    0.04236   3.991 0.000102 ***
## alpha   0.80138    0.37035   2.164 0.032018 *  
## A      14.44405   17.75070   0.814 0.417063    
## k     322.91440  267.39188   1.208 0.229035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.058 on 154 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.138e-06
##   (163 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) : 
##   Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value Pr(>F)
## 1    154     172.37                          
## 2    153     171.91  1 0.45685  0.4066 0.5247
##   model      AIC
## 1     3 546.5272
## 2    3a 548.1052
## 3    3b 548.4791
## 4    3c       NA
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##        Estimate Std. Error t value Pr(>|t|)    
## ge     -0.68834    4.20877  -0.164 0.870301    
## phi     0.16904    0.04236   3.991 0.000102 ***
## alpha   0.80138    0.37035   2.164 0.032018 *  
## A      14.44405   17.75070   0.814 0.417063    
## k     322.91440  267.39188   1.208 0.229035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.058 on 154 degrees of freedom
## 
## Number of iterations to convergence: 7 
## Achieved convergence tolerance: 5.138e-06
##   (163 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: does not fit

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.96832, p-value = 0.001033
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = 1.977, p-value = 0.04804
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 90 rows containing missing values (geom_point).
## Warning: Removed 1274 row(s) containing missing values (geom_path).

plotting 2

M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M313$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M313.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow

model selection 1

## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`",  : 
##   missing value where TRUE/FALSE needed
##   model AIC
## 1     1  NA
## 2     2  NA
## 3     3  NA
## Warning in min(AIC1_M331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in h(simpleError(msg, call)) : 
##   error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_M331.' not found

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2

M334 - Black Hills Coniferous Forest

model selection 1

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
##   Res.Df Res.Sum Sq Df  Sum Sq F value   Pr(>F)   
## 1    180     187.48                               
## 2    179     187.45  1  0.0346   0.033 0.856041   
## 3    178     176.90  1 10.5461  10.612 0.001346 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     1 561.9578
## 2     2 563.9241
## 3     3 555.3271
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + 
##     B_plt_t1_MgHa)
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     5.34143   10.68436   0.500 0.617742    
## phi   -0.04759    0.05520  -0.862 0.389777    
## alpha  0.90924    0.24954   3.644 0.000352 ***
## A      1.29761    1.34860   0.962 0.337258    
## k     41.52941   17.19855   2.415 0.016760 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9969 on 178 degrees of freedom
## 
## Number of iterations to convergence: 9 
## Achieved convergence tolerance: 6.029e-06
##   (75 observations deleted due to missingness)

summary

  • simple model: fits
  • phi model: fits
  • phi-alpha model: fits

model selection 2

## Analysis of Variance Table
## 
## Model 1: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##   Res.Df Res.Sum Sq Df  Sum Sq F value  Pr(>F)  
## 1    178     176.90                             
## 2    177     176.82  1 0.08245  0.0825 0.77422  
## 3    177     175.67  0 0.00000                  
## 4    176     172.74  1 2.93465  2.9901 0.08553 .
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##   model      AIC
## 1     3 555.3271
## 2    3a 557.2418
## 3    3b 556.0501
## 4    3c 554.9672
## 
## Formula: G_MassBal_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + 
##     phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - 
##     p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## 
## Parameters:
##       Estimate Std. Error t value Pr(>|t|)    
## ge     4.24357    8.41669   0.504 0.614762    
## phi   -0.04452    0.05422  -0.821 0.412714    
## alpha  0.93202    0.24607   3.788 0.000209 ***
## A      1.08465    0.98015   1.107 0.269972    
## k     35.67916    6.75553   5.281 3.75e-07 ***
## p      0.22887    0.10184   2.247 0.025852 *  
## s      3.22389    1.93656   1.665 0.097742 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9907 on 176 degrees of freedom
## 
## Number of iterations to convergence: 10 
## Achieved convergence tolerance: 5.967e-06
##   (75 observations deleted due to missingness)

summary

  • add p model: fits
  • add s model: fits
  • add s+p model: fits

plot residuals

## 
## ------
##  Shapiro-Wilk normality test
## 
## data:  stdres
## W = 0.72367, p-value < 2.2e-16
## 
## 
## ------
## 
##  Runs Test
## 
## data:  as.factor(run)
## Standard Normal = -0.21879, p-value = 0.8268
## alternative hypothesis: two.sided

predict and plot

## Warning: Removed 33 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_segment).
## Warning: Removed 1264 row(s) containing missing values (geom_path).

plotting 2

## Warning: Removed 1 rows containing missing values (geom_segment).

M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow

model selection 1

summary

  • simple model: does not fit
  • phi model: does not fit
  • phi-alpha model: does not fit

model selection 2

summary

  • add p model: does not fit
  • add s model: does not fit
  • add s+p model: does not fit

plot residuals

## [1] "cannot plot residuals"

predict and plot

## [1] "cannot plot data with prediction"

plotting 2


Fitted parameters

Best / selected models by ecoprovince

Code Ecoregion Sel.Mod
211 Northeastern Mixed Forest 3b
212 Laurentian Mixed Forest 3a
221 Eastern Broadleaf Forest 3a
222 Midwest Broadleaf Forest 3a
223 Central Interior Broadleaf Forest 3
231 Southeastern Mixed Forest 3b
232 Outer Coastal Plain Mixed Forest 3a
234 Lower Mississippi Riverine Forest 1
242 Pacific Lowland Mixed Forest NA
251 Prairie Parkland (Temperate) 1
255 Prairie Parkland (Subtropical) NA
261 California Coastal Chaparral Forest and Shrub NA
262 California Dry Steppe NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest NA
313 Colorado Plateau Semi-Desert NA
315 Southwest Plateau and Plains Dry Steppe and Shrub NA
321 Chihuahuan Semi-Desert NA
322 American Semidesert and Desert NA
331 Great Plains/Palouse Dry Steppe 3
332 Great Plains Steppe 1a
341 Intermountain Semi-Desert and Desert NA
342 Intermountain Semi-Desert NA
411 Everglades NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow 3a
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow 3
M223 Ozark Broadleaf Forest Meadow 1a
M231 Ouachita Mixed Forest 3
M242 Cascade Mixed Forest NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow 3
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow NA
M334 Black Hills Coniferous Forest 3c
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow NA

table by ecoprovince

Code Ecoregion region n.obs n.plots ge ge.variance ge.2.5 ge.97.5 phi phi.variance phi.2.5 phi.97.5 alpha alpha.variance alpha.2.5 alpha.97.5 A A.2.5 A.97.5 k k.2.5 k.97.5
211 Northeastern Mixed Forest east 4834 2417 -0.0701777 0.0378473 -0.4516004 0.3112450 0.0081316 0.0000419 -0.0045648 0.0208281 0.5233081 0.0094110 0.3331092 0.7135070 3.8560322 3.3955220 4.316542 7.2130845 4.9140132 9.5121557
212 Laurentian Mixed Forest east 12976 6488 0.6460311 0.0434727 0.2373137 1.0547485 0.0171509 0.0000238 0.0075877 0.0267141 0.5747427 0.0032763 0.4625398 0.6869456 2.9832899 2.7390098 3.227570 25.1990149 19.7462922 30.6517376
221 Eastern Broadleaf Forest east 5462 2731 -0.9996150 0.0207816 -1.2822371 -0.7169930 0.0182832 0.0000521 0.0041306 0.0324358 0.5862302 0.0074067 0.4175057 0.7549547 7.6162619 5.7511807 9.481343 199.6435884 41.8356816 357.4514952
222 Midwest Broadleaf Forest east 3554 1777 -0.3371896 0.0833952 -0.9035127 0.2291336 0.0166786 0.0001668 -0.0086511 0.0420083 0.7313236 0.0080930 0.5549034 0.9077438 6.1529187 4.9328446 7.372993 112.1183167 55.6243232 168.6123103
223 Central Interior Broadleaf Forest east 6390 3195 -1.0271460 0.0219393 -1.3175365 -0.7367556 -0.0185398 0.0000921 -0.0373497 0.0002701 0.5344246 0.0094325 0.3440166 0.7248326 5.6438245 5.1405654 6.147083 33.3069888 25.7469229 40.8670546
231 Southeastern Mixed Forest east 8200 4100 0.5717335 0.0376410 0.1914023 0.9520647 0.0041198 0.0000443 -0.0089209 0.0171605 0.7207891 0.0058020 0.5714682 0.8701099 8.1321892 0.8942751 15.370103 32.2539036 -234.5665566 299.0743637
232 Outer Coastal Plain Mixed Forest east 8194 4097 0.4993901 0.0462372 0.0778623 0.9209178 -0.0029963 0.0000463 -0.0163320 0.0103395 0.6469230 0.0043235 0.5180241 0.7758220 5.3376805 4.8148740 5.860487 40.9241269 25.0560111 56.7922428
234 Lower Mississippi Riverine Forest east 862 431 0.3086104 0.5636793 -1.1655112 1.7827320 NA NA NA NA NA NA NA NA 3.9841392 2.7849147 5.183364 0.0839457 -0.3513901 0.5192815
242 Pacific Lowland Mixed Forest pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
251 Prairie Parkland (Temperate) east 1394 697 -0.2615823 0.2834626 -1.3065478 0.7833832 NA NA NA NA NA NA NA NA 3.4267952 2.5608351 4.292755 12.2112022 4.0960249 20.3263795
255 Prairie Parkland (Subtropical) east 446 223 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
261 California Coastal Chaparral Forest and Shrub pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
262 California Dry Steppe pacific 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
263 California Coastal Steppe - Mixed Forest and Redwood Forest pacific 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
313 Colorado Plateau Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
315 Southwest Plateau and Plains Dry Steppe and Shrub interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
321 Chihuahuan Semi-Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
322 American Semidesert and Desert interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
331 Great Plains/Palouse Dry Steppe interior west 118 59 0.8753568 104.2515550 -19.3768540 21.1275675 0.2478384 0.0267117 -0.0763383 0.5720151 1.0137067 0.3387254 -0.1406899 2.1681033 0.7672107 -1.8583073 3.392729 8.1068470 -17.5967287 33.8104226
332 Great Plains Steppe interior west 154 77 -0.1567804 1.6399531 -2.6908696 2.3773089 NA NA NA NA NA NA NA NA 5.2350165 0.2501706 10.219862 137.1513327 -89.0640077 363.3666731
341 Intermountain Semi-Desert and Desert interior west 4 2 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
342 Intermountain Semi-Desert interior west 2 1 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
411 Everglades east 66 33 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M211 Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow east 5104 2552 0.8972259 0.0678505 0.3865352 1.4079167 0.0150869 0.0000326 0.0039012 0.0262725 0.4453919 0.0079754 0.2703037 0.6204800 2.7988408 2.5301790 3.067503 4.9381866 0.5938972 9.2824760
M221 Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow east 5262 2631 -0.0813187 0.0490861 -0.5156692 0.3530318 -0.0098383 0.0000891 -0.0283479 0.0086713 0.8086234 0.0147504 0.5705216 1.0467251 4.3449555 3.9288933 4.761018 9.5835344 5.1332003 14.0338684
M223 Ozark Broadleaf Forest Meadow east 604 302 2.6616500 2.6268365 -0.5223335 5.8456335 NA NA NA NA NA NA NA NA 3.6416527 -5.1580948 12.441400 344.4875424 -1574.5518250 2263.5269097
M231 Ouachita Mixed Forest east 678 339 2.7238765 4.0976205 -1.2519071 6.6996602 0.0737275 0.0010431 0.0102925 0.1371624 0.8879001 0.1360306 0.1635056 1.6122946 2.1186016 0.9531822 3.284021 20.1995348 7.0597838 33.3392857
M242 Cascade Mixed Forest pacific 34 17 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M261 Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow pacific 340 170 -0.6883394 17.7137530 -9.0027162 7.6260374 0.1690382 0.0017940 0.0853659 0.2527105 0.8013844 0.1371615 0.0697561 1.5330127 14.4440524 -20.6222516 49.510356 322.9143977 -205.3150747 851.1438701
M262 California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow interior west 8 4 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M313 Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M331 Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M332 Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 20 10 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M333 Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow interior west 22 11 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
M334 Black Hills Coniferous Forest interior west 310 155 4.2435694 70.8407109 -12.3670625 20.8542013 -0.0445205 0.0029400 -0.1515296 0.0624887 0.9320177 0.0605519 0.4463843 1.4176510 1.0846462 -0.8497134 3.019006 35.6791576 22.3468885 49.0114267
M341 Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow interior west 0 0 NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

plot ge

map

## OGR data source with driver: ESRI Shapefile 
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings:  PROVINCE_ PROVINCE_I
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database

plot phi (effect of DeltaPDSI)

plot alpha (biomass growth compensation effect)

plot A (asymptote of forest biomass growth in Mg/ha/yr)

## Warning: Removed 19 rows containing missing values (geom_point).

plot k (stand biomass at half biomss G in Mg/ha)

## Warning: Removed 19 rows containing missing values (geom_point).

Caclulations - weighted averages

ge (stand biomass growth enhancement factor in % 2000-2021)

##          region  weighted.ge weighted.ge.std_Error 95 % CI, upper
## 1     entire US  0.188648990            0.08924345     0.36356614
## 2       pacific -0.003598219            0.02200089     0.03952353
## 3          east  0.170804842            0.07428861     0.31641052
## 4 interior west  0.021442367            0.04428945     0.10824968
##   95 % CI, lower
## 1     0.01373184
## 2    -0.04671997
## 3     0.02519916
## 4    -0.06536495

phi (effect of DeltaPDSI)

##          region weighted.phi weighted.phi.std_Error 95 % CI, upper
## 1     entire US 0.0070707690           0.0023391806    0.011655563
## 2       pacific 0.0008836290           0.0002214075    0.001317588
## 3          east 0.0059496998           0.0022952212    0.010448333
## 4 interior west 0.0002374402           0.0003933247    0.001008357
##   95 % CI, lower
## 1   0.0024859751
## 2   0.0004496703
## 3   0.0014510663
## 4  -0.0005334762

alpha (biomass growth compensation effect)

##          region weighted.alpha weighted.alpha.std_Error 95 % CI, upper
## 1     entire US    0.587716290              0.026025563    0.638726393
## 2       pacific    0.004189150              0.001935981    0.007983673
## 3          east    0.577245924              0.025905434    0.628020575
## 4 interior west    0.006281216              0.001578093    0.009374278
##   95 % CI, lower
## 1   0.5367061877
## 2   0.0003946271
## 3   0.5264712737
## 4   0.0031881538

A (asymptote of forest biomass growth in Mg/ha/yr)

##          region weighted.A
## 1     entire US   4.957463
## 2       pacific  12.992005
## 3          east   4.940171
## 4 interior west   1.932545

K (stand biomass at half biomass G in Mg/ha)

##          region weighted.k
## 1     entire US   47.98194
## 2       pacific  290.45210
## 3          east   46.51098
## 4 interior west   51.94115